A spatial generalization of the method of conformal mappings for the solution of model boundary-value filtration problems

Journal of Water and Land Development

“…( 9)) again. Similarly, to BOMBA et al [2007;2008;2018], we achieve the optimality of the relation between m and n by optimising the analogues of functional equations (for example, Riemann's functional equation). The rationale for the constructed algorithm for "alternating fixation of the process and environment characteristics, the conformal parameter, internal and boundary nodes of the curvilinear area" is the same as in papers by BOMBA et al [2007;2008;2018], with the use of ideas of block iterative methods described by SAMARSKIY [1977].…”

“…Taking into account the research results revealed in BOMBA et al [2007;2008;2018], putting a harmonic function ψ = ψ(x, y) (flow function), complex conjugate to φ = φ(x, y), and by the adoption of a number of boundary conditions, form a more general the corresponding conformal mapping problem ω = ω(z) = φ(x, y) + iψ(x, y) of the considered area G z to the corresponding complex potential area G ω ={ω:…”

“…Similarly to other researchers, like POLUBARINOVA-KOCHINA [1948], SAMARSKIY [1977], MARCHUK [1989] andBOMBA et al [2007;2008;2018], we shall describe the noted fragment with the equation of motion � ¼ k f grad' (Darcy's law) and the continuity equation div� ¼ 0, where…”

“…( 6) -Eq. ( 9)) following the schemes suggested by BOMBA et al [2007;2008;2018]. We assign the quantities of m and n nodes partitioning the grid domain G ω , parameter ε, which characterises the approximation accuracy of the solution of the corresponding difference problem.…”